Article
Mathematics
Leon Simon
Summary: With respect to a C infinity metric close to the standard Euclidean metric, a class of embedded (N + )-dimensional pound hypersurfaces without boundary is constructed, which are minimal and strictly stable, and have a singular set equal to an arbitrary preassigned closed subset K C {0} x Re. This settles the question of whether there can be gaps or fractional dimensional parts in the singular set with a strong affirmative. The construction involves the analysis of solutions u of the symmetric minimal surface equation on domains 52 C Rn whose symmetric graphs lie on one side of a cylindrical minimal cone.
ANNALS OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Lei Ni
Summary: This study explores the properties of plurisubharmonic functions based on the consequences of the Liouville theorem, including a nonlinear version of the complex splitting theorem, k-hyperbolicity and its connection with the negativity of the k-scalar curvature, and a new Schwarz lemma-type estimate in terms of only the holomorphic sectional curvatures.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2021)
Article
Mathematics
Pascal Collin, Laurent Hauswirth, Minh Hoang Nguyen
Summary: In this paper, we construct complete and embedded minimal annuli that approach vertical planes in the Riemannian 3-manifold (PSL) over tilde (2)(R, tau). The boundary of these annuli is composed of 4 vertical lines at infinity. They are constructed by taking the limit of a sequence of compact minimal annuli. The compactness is obtained from a curvature estimate, which uses foliations by minimal surfaces and is independent of the index of the surface. We also prove the existence of a one-periodic family of Riemann's type examples. The difficulty of the construction lies in the lack of symmetry of the ambient space (PSL) over tilde (2)(R, tau).
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics
Ankit Bhojak, Parasar Mohanty
Summary: This paper presents proofs that for Omega is an element of L log L(Sd-1), the rough maximal singular integral operator T Omega* is of weak type L log log L(Rd). Furthermore, for w is an element of A1 and Omega is an element of L infinity(Sd-1), it is shown that T Omega* is of weak type L log log L(w) with weight dependence [w]A1[w]A infinity log([w]A infinity + 1), which is same as the best known constant for the singular integral T Omega.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics
Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang
Summary: The sunflower lemma states that for a family of sets of size w, containing at least about w(w) sets, there must be a sunflower with r petals. This paper presents a new definition for sunflowers and improves the bound on the number of sets to about (log w)(w).
ANNALS OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Minghua Lin, Mengyan Xie
Summary: In this note, we propose a simple idea to improve the lower bound for the smallest singular value of matrices, which is shown to be close to the exact value through numerical examples. We compare our bound with existing ones and discuss potential improvements in this area.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics
Istvan Tomon
Summary: This paper investigates the piercing number and independence number of axis-parallel box families. For a given dimension d, a new box family is constructed to explore the related Ramsey and coloring properties.
ADVANCES IN MATHEMATICS
(2023)
Article
Automation & Control Systems
Zhihao Zhang, Zhiguang Feng
Summary: This article studies the reachable set estimation problem for discrete-time singular systems. By decomposing and reconstructing the systems, singular systems are transformed into dynamic systems with algebraic equations. Two novel reachable set estimation methods based on ellipsoidal sets are proposed for systems with nonzero initial conditions. A series of enclosing ellipsoidal sets can be obtained to bound the real-time states of the considered systems. The effectiveness of the proposed methods is illustrated through a numerical example.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Engineering, Electrical & Electronic
Ori Aharon, Joseph Tabrikian
Summary: This article derives a new class of global mean-squared-error (MSE) lower bound for Bayesian parameter estimation. The Hammersley-Chapman-Robbins (HCR) bound is shown to be related to the ambiguity function in the non-Bayesian framework. Based on this observation, a new class of Bayesian MSE lower bound is derived by substituting shift test-points with arbitrary transformations. The proposed bound accurately predicts the threshold phenomenon and outperforms the Weiss-Weinstein bound in threshold prediction and asymptotic performance in both frequency and direction-of-arrival estimation problems.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2023)
Article
Automation & Control Systems
Xiuyang Chen, Changbing Tang, Zhao Zhang
Summary: This paper studies the minimum secure dominating set problem in wireless networks using algorithmic game theory. By designing a game framework for SDS and proving that every Nash equilibrium is a minimal dominating set, the authors provide an effective solution to the problem.
IEEE-CAA JOURNAL OF AUTOMATICA SINICA
(2023)
Article
Physics, Particles & Fields
Gauhar Abbas, Vartika Singh, Neelam Singh, Ria Sain
Summary: We investigate the flavour bounds on Z(2) Z(5) and Z(2) Z(9) flavour symmetries, which are minimal and non-minimal forms of the Z2 ZN flavour symmetry. These symmetries can explain the masses and mixing pattern of fermions, including neutrinos, in the standard model. We derive bounds on the flavon field of these symmetries using current quark and lepton flavour physics data and future sensitivities. The strongest bounds come from D-0 - (D) over bar (0) mixing for the Z(2) Z(5) symmetry.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Mathematics, Applied
Xu Shun
Summary: This paper presents two new lower bounds for the smallest singular value of non-singular matrices, which outperform the bounds proposed by Zou [1], Lin, and Xie [2] under certain circumstances.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2022)
Article
Mathematics
Laxman Saha, Mithun Basak, Kalishankar Tiwary, Kinkar Chandra Das, Yilun Shang
Summary: In this article, the concept of metric dimension and metric basis of a simple connected graph is discussed. The metric dimension of power of finite paths is determined and all metric bases for the same are characterized.
Article
Mathematics, Applied
Susanne Bradley, Chen Greif
Summary: This paper derives upper bounds on the eigenvalues of saddle-point matrices with singular leading blocks by augmenting the singular leading block to replace it with a positive definite matrix. The bounds are dependent on the principal angles between the ranges or kernels of the matrix blocks. Numerical experiments validate the analytical findings.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Physics, Mathematical
Svetlana Jitomirskaya, Wencai Liu
Summary: This study presents a simple method, not based on transfer matrices, to demonstrate the vanishing of dynamical transport exponents, which is applied to long-range quasiperiodic operators. Published by AIP Publishing under an exclusive license.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Davide Parise, Alessandro Pigati, Daniel Stern
Summary: This paper studies the self-dual Yang-Mills-Higgs energies on a closed Riemannian manifold and proves their convergence to minimal submanifolds. The author establishes a connection between the energies and the Euler class by introducing a suitable gauge invariant Jacobian, and shows the existence of a recovery sequence under certain conditions. Furthermore, a comparison between the min-max values obtained from the Almgren-Pitts theory and the Yang-Mills-Higgs framework is made, with the former always providing a lower bound for the latter.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Wenkui Du, Robert Haslhofer
Summary: This paper explores ancient noncollapsed mean curvature flows and provides insights into their behavior and properties through spectral analysis and precise asymptotic analysis in various cases.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2024)
